The Scanning Tunnelling Microscope (STM)
The TEM reaches atomic-scale imaging through a short electron wavelength. The STM gets there by an entirely different route — no beam, no wavelength, no lenses — by exploiting one of the strangest effects in quantum mechanics: a particle crossing a barrier it classically has no right to cross.
A completely different principle from the TEM
It's worth being explicit about this from the outset: the scanning tunnelling microscope does not work anything like the transmission electron microscope covered in the previous lesson. The TEM's entire operating principle rests on the short de Broglie wavelength of a fast-moving electron beam, focused by electromagnetic lenses and transmitted through a sample. The STM uses none of that — there is no beam, no accelerating voltage in the electron-gun sense, no wavelength-based imaging, and no lenses at all. Instead, the STM relies on a purely quantum-mechanical effect that has nothing to do with wave-particle duality or de Broglie wavelengths as such: quantum tunnelling.
The tunnelling current
An STM uses an extremely sharp conducting tip — ideally, in the best instruments, narrowing down to a single atom at its very point — mounted so it can be moved with sub-atomic precision in all three directions. This tip is brought to within about a nanometre of the surface of a conducting sample, close enough that a gap remains between tip and surface, but small enough for something remarkable to happen: electrons can cross that gap, from tip to sample or sample to tip, even though classically they do not have enough energy to escape either surface and cross the empty space between them.
This crossing is quantum tunnelling — a purely quantum-mechanical effect in which a particle has a genuine, non-zero probability of passing through (or across) a region that a classical particle with the same energy could never enter. With a small voltage applied between tip and sample, this tunnelling of electrons across the gap becomes a continuous, measurable flow: the tunnelling current.
Classically, an electron confined to a conductor simply does not have enough energy to exist in the empty space of the gap between tip and sample — it would need to "borrow" energy it doesn't have to get there, which classical mechanics forbids outright. Quantum mechanics treats the electron's position as described by a wavefunction that extends, with rapidly decreasing amplitude, into and through the classically forbidden gap. That non-zero (if small) amplitude on the far side of the gap corresponds to a real, non-zero probability of the electron appearing there — which is exactly what produces a measurable tunnelling current in practice.
Extreme sensitivity to gap width
The size of the tunnelling current depends extremely sensitively on the width of the gap between tip and surface — far more sensitively than most everyday physical quantities depend on distance. As a rough guide, the tunnelling current changes by roughly an order of magnitude for every $0.1\,\text{nm}$ change in gap width — a change in separation smaller than the diameter of a single atom. This means even the tiniest variation in the height of the sample's surface, right down to the scale of individual atoms sitting slightly higher or lower than their neighbours, produces an easily measurable change in the tunnelling current.
This extreme sensitivity is precisely what gives the STM its atomic-scale resolution — not a short wavelength, as in the TEM, but a current that reacts so strongly to distance that atomic-scale bumps and dips in a surface are impossible for it to miss.
Scanning and imaging the surface
To build up an image, the tip is scanned across the sample's surface line by line, moving in a raster pattern (back and forth, stepping down slightly after each pass) so that eventually the whole area of interest has been covered. As the tip moves, a feedback system continuously monitors the tunnelling current and adjusts the tip's height above the surface, in real time, to keep that current — and therefore the gap width — constant.
Because the feedback system is constantly correcting the tip's height to hold the gap (and current) fixed, the height adjustments it makes at every point along the scan directly trace out the height of the surface underneath the tip at that point: where the surface bulges upward, the tip is pulled back to maintain the same gap; where the surface dips down, the tip is lowered to follow it. Recording the tip's height at every point of the scan therefore builds up a complete, point-by-point map of the surface's topography, down to atomic-scale detail.
The TEM and STM reach atomic-scale imaging by entirely different physical mechanisms: the TEM exploits the short de Broglie wavelength of a fast-moving electron beam to form a transmission image, much like an extreme version of an optical microscope; the STM exploits quantum tunnelling of electrons across a vacuum gap, with no beam or wavelength-based imaging involved at all.
Both instruments, despite their completely different operating principles, only became possible once quantum mechanics — first hinted at by the wave-particle duality covered several lessons back in this module — was understood well enough, and precisely enough, to be engineered into working laboratory instruments. Neither a TEM nor an STM could have been built, or even conceived, on classical physics alone.
Key takeaways
- The STM works on a completely different principle from the TEM — no electron beam, no de Broglie wavelength, no lenses.
- A sharp conducting tip, ideally ending in a single atom, is brought to within about a nanometre of a conducting sample's surface.
- Electrons cross the gap between tip and surface by quantum tunnelling, a purely quantum-mechanical effect, despite classically lacking enough energy to do so.
- A small applied voltage turns this tunnelling into a measurable, continuous tunnelling current.
- The tunnelling current is extremely sensitive to gap width, changing by roughly an order of magnitude per $0.1\,\text{nm}$ change in separation — this sensitivity is the source of the STM's atomic-scale resolution.
- Scanning the tip line by line across the surface, while a feedback system holds the tunnelling current (and hence the gap) constant, traces out the tip's height at every point and so maps the surface's atomic-scale topography.
- Both the TEM and STM only became possible once quantum mechanics — first hinted at by wave-particle duality — was understood well enough to engineer into working instruments.